Algebra Examples

$\frac{x}{3} = 5 + \frac{x - 35}{5}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $5$ from both sides of the equation.

$\frac{x}{3} - 5 = \frac{x - 35}{5}$

Step 1.2

Subtract $\frac{x - 35}{5}$ from both sides of the equation.

$\frac{x}{3} - 5 - \frac{x - 35}{5} = 0$

Step 2

Simplify $\frac{x}{3} - 5 - \frac{x - 35}{5}$ .

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Step 2.1

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{3} \cdot \frac{5}{5} - \frac{x - 35}{5} - 5 = 0$

Step 2.2

To write $- \frac{x - 35}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{3} \cdot \frac{5}{5} - \frac{x - 35}{5} \cdot \frac{3}{3} - 5 = 0$

Step 2.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{x}{3}$ by $\frac{5}{5}$ .

$\frac{x \cdot 5}{3 \cdot 5} - \frac{x - 35}{5} \cdot \frac{3}{3} - 5 = 0$

Step 2.3.2

Multiply $3$ by $5$ .

$\frac{x \cdot 5}{15} - \frac{x - 35}{5} \cdot \frac{3}{3} - 5 = 0$

Step 2.3.3

Multiply $\frac{x - 35}{5}$ by $\frac{3}{3}$ .

$\frac{x \cdot 5}{15} - \frac{(x - 35) \cdot 3}{5 \cdot 3} - 5 = 0$

Step 2.3.4

Multiply $5$ by $3$ .

$\frac{x \cdot 5}{15} - \frac{(x - 35) \cdot 3}{15} - 5 = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x \cdot 5 - (x - 35) \cdot 3}{15} - 5 = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Move $5$ to the left of $x$ .

$\frac{5 \cdot x - (x - 35) \cdot 3}{15} - 5 = 0$

Step 2.5.2

Apply the distributive property.

$\frac{5 x + (- x - - 35) \cdot 3}{15} - 5 = 0$

Step 2.5.3

Multiply $- 1$ by $- 35$ .

$\frac{5 x + (- x + 35) \cdot 3}{15} - 5 = 0$

Step 2.5.4

Apply the distributive property.

$\frac{5 x - x \cdot 3 + 35 \cdot 3}{15} - 5 = 0$

Step 2.5.5

Multiply $3$ by $- 1$ .

$\frac{5 x - 3 x + 35 \cdot 3}{15} - 5 = 0$

Step 2.5.6

Multiply $35$ by $3$ .

$\frac{5 x - 3 x + 105}{15} - 5 = 0$

Step 2.5.7

Subtract $3 x$ from $5 x$ .

$\frac{2 x + 105}{15} - 5 = 0$

Step 2.6

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{2 x + 105}{15} - 5 \cdot \frac{15}{15} = 0$

Step 2.7

Combine $- 5$ and $\frac{15}{15}$ .

$\frac{2 x + 105}{15} + \frac{- 5 \cdot 15}{15} = 0$

Step 2.8

Combine the numerators over the common denominator.

$\frac{2 x + 105 - 5 \cdot 15}{15} = 0$

Step 2.9

Simplify the numerator.

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Step 2.9.1

Multiply $- 5$ by $15$ .

$\frac{2 x + 105 - 75}{15} = 0$

Step 2.9.2

Subtract $75$ from $105$ .

$\frac{2 x + 30}{15} = 0$

Step 2.9.3

Factor $2$ out of $2 x + 30$ .

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Step 2.9.3.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 30}{15} = 0$

Step 2.9.3.2

Factor $2$ out of $30$ .

$\frac{2 x + 2 \cdot 15}{15} = 0$

Step 2.9.3.3

Factor $2$ out of $2 x + 2 \cdot 15$ .

$\frac{2 (x + 15)}{15} = 0$